Decision makers usually have to face a budget and other type of constraints when they have to decide which projects are going to be undertaken (to satisfy their requirements and guarantee profitable growth). Our purpo...
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Decision makers usually have to face a budget and other type of constraints when they have to decide which projects are going to be undertaken (to satisfy their requirements and guarantee profitable growth). Our purpose is to assist them in the task of selecting project portfolios. We have approached this problem by proposing a general nonlinear binary multi-objective mathematical model, which takes into account all the most important factors mentioned in the literature related with Project Portfolio Selection and Scheduling. Due to the existence of uncertainty in different aspects involved in the aforementioned decision task, we have also incorporated into the model some fuzzy parameters, which allow us to represent information not fully known by the decision maker/s. The resulting problem is both fuzzy and multiobjective. The results are complemented with graphical tools, which show the usefulness of the proposed model to assist the decision maker/s.
Approximately twenty years ago the modern interest for hierarchical programming was initiated by J. Bracken and J.M. McGill [9], [10]. The activities in the field have ever grown lively, both in terms of theoretical d...
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Approximately twenty years ago the modern interest for hierarchical programming was initiated by J. Bracken and J.M. McGill [9], [10]. The activities in the field have ever grown lively, both in terms of theoretical developments and terms of the diversity of the applications. The collection of seven papers in this issue covers a diverse number of topics and provides a good picture of recent research activities in the field of bilevel and hierarchical programming. The papers can be roughly divided into three categories;Linear bilevel programming is addressed in the first two papers by Gendreau et al and Moshirvaziri et al;The following three papers by Nicholls, Loridan & Morgan, and Kalashnikov & Kalashnikova are concerned with nonlinear bilevel programming;and, finally, Wen & Lin and Nagase & Aiyoshi address hierarchical decision making issues relating to both biobjective and bilevel programming.
This paper deals with multiobjective programming in which the objective functions are nonsymmetric distances (derived from different gauges) to the points of a fixed finite subset of ?n. It emphasizes the case in whic...
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This paper deals with multiobjective programming in which the objective functions are nonsymmetric distances (derived from different gauges) to the points of a fixed finite subset of ?n. It emphasizes the case in which the gauges are polyhedral. In this framework the following result is known: if the gauges are polyhedral, then each Pareto optimum is the solution to a Fermat—Weber problem with strictly positive coefficients. We give a new proof of this result, and we show that it is useful in finding the whole set of efficient points of a location problem with polyhedral gauges. Also, we characterize polyhedral gauges in terms of a property of their subdifferential.
We propose two strategies for choosing Pareto solutions of constrained multiobjective optimization problems. The first one, for general problems, furnishes balanced optima, i.e. feasible points that, in some sense, ha...
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We propose two strategies for choosing Pareto solutions of constrained multiobjective optimization problems. The first one, for general problems, furnishes balanced optima, i.e. feasible points that, in some sense, have the closest image to the vector whose coordinates are the objective components infima. It consists of solving a single scalar-valued problem, whose objective requires the use of a monotonic function which can be chosen within a large class of functions. The second one, for practical problems for which there is a preference among the objective's components to be minimized, gives us points that satisfy this order criterion. The procedure requires the sequential minimization of all these functions. We also study other special Pareto solutions, the sub-balanced points, which are a generalization of the balanced optima.
In this paper a mathematical programming model for long term forest planning is presented. The model uses aggregated data and is intended to be used in analyzing the effects of different strategic decisions. The objec...
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In this paper a mathematical programming model for long term forest planning is presented. The model uses aggregated data and is intended to be used in analyzing the effects of different strategic decisions. The objectives, which are formulated by headquarters, may be both short term as well as long term 'goals' or 'targets'. Some of the objectives are in conflict with one another, while others may be complementary. The complexity of the problem and the effects of various objectives are analyzed with the help of multiobjective programming techniques. A discussion on how the objectives may change during the problem analysis is held and two different approaches are used to conduct the analysis. The pros and tons of the two methods and their usefulness in solving a practical forest management problem is presented based on a practical problem with data from a subunit of the Swedish Forest Service (SFS). [ABSTRACT FROM AUTHOR]
We develop an approach which enables the decision maker to search for a compromise solution to a multiobjective stochastic linear programming (MOSLP) problem where the objective functions depend on parameters which ar...
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We develop an approach which enables the decision maker to search for a compromise solution to a multiobjective stochastic linear programming (MOSLP) problem where the objective functions depend on parameters which are continuous random variables with normal multivariate distributions. The minimum-risk criterion is used to transform the MOSLP problem into its corresponding deterministic equivalent which in turn is reduced to a Chebyshev problem. An algorithm based on the combined use of the bisection method and the probabilities of achieving goals is developed to obtain the optimal or epsilon optimal solution of this specific problem. An illustrated example is included in this paper to clarify the developed theory.
Existing cropping systems in Northern Zambia cause deforestation and soil degradation. To reduce the environmental problems, the potential of alley cropping and pigeon peas replacing the existing cropping systems was ...
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Existing cropping systems in Northern Zambia cause deforestation and soil degradation. To reduce the environmental problems, the potential of alley cropping and pigeon peas replacing the existing cropping systems was analyzed by the use of multi-objective programming models of peasant households. The models were formulated based on the theories of Chayanov and Nakajima which are suitable under conditions of imperfect labour markets. Risk was incorporated in the models in relation to weather and fertilizer supply. The models provide an opportunity to relate key characteristics of new technologies to key characteristics of peasants' preferences and resource constraints. The models may also be used to identify minimum performance levels required for new technologies to be found acceptable. Models of a small male-headed household are presented under varying conditions: for high and low population densities, with and without fertilizer subsidies, and for households with and without access to off-farm employment under high population density conditions. The analysis showed that the alley cropping technology is very unlikely to replace the chitemene system where there is still sufficient woodland for its continuation. The technology may have higher potential in more densely populated areas, where more intensive forms of agriculture are practised and where there is access to inputs such as lime and fertilizer. The removal of fertilizer subsides as a result of the Structural Adjustment Programs, may favour alley cropping because this technology may increase the efficiency of fertilizer use and reduce the need for nitrogenous fertilizers. The potential of the technology depends very much on the management level and location-specific performance of the trees. The pigeon pea technology has high potential if it is accepted as food since it has a very favourable yield per unit of labour, requires no monetary inputs, and can grow in very poor soils. Pigeon pea also has potential a
The paper discusses a scalar problem that uses a reference point for solving the multiobjective nonlinear programming (MONLP) problem. Some properties of the solution of this scalar problem are described. In order to ...
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The paper discusses a scalar problem that uses a reference point for solving the multiobjective nonlinear programming (MONLP) problem. Some properties of the solution of this scalar problem are described. In order to improve the achieved value of one criterion, only the corresponding component of the reference point has to be changed.
Many classes of mathematical programming problems can be formulated as a linear program with a parametric objective function. Gass and Saaty developed in the early 1950's a parametric programming procedure for sol...
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Many classes of mathematical programming problems can be formulated as a linear program with a parametric objective function. Gass and Saaty developed in the early 1950's a parametric programming procedure for solving the latter problem. This procedure is relevant to solution strategies for many problem types but is underutilized, often because the relationship of the procedure to the relevant problem class is not recognized. In this paper five recent applications of the parametric programming procedure are presented.
Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stab...
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Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we define a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufficient conditions on when strict locally efficient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions.
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